49 lines
809 B
Markdown
49 lines
809 B
Markdown
|
---
|
||
|
|
id: 5900f4e61000cf542c50fff9
|
||
|
|
title: 'Problem 378: Triangle Triples'
|
||
|
|
challengeType: 5
|
||
|
|
forumTopicId: 302040
|
||
|
|
dashedName: problem-378-triangle-triples
|
||
|
|
---
|
||
|
|
|
||
|
|
# --description--
|
||
|
|
|
||
|
|
Let T(n) be the nth triangle number, so T(n) =
|
||
|
|
|
||
|
|
n (n+1)2
|
||
|
|
|
||
|
|
.
|
||
|
|
|
||
|
|
Let dT(n) be the number of divisors of T(n). E.g.: T(7) = 28 and dT(7) = 6.
|
||
|
|
|
||
|
|
Let Tr(n) be the number of triples (i, j, k) such that 1 ≤ i < j < k ≤ n and dT(i) > dT(j) > dT(k). Tr(20) = 14, Tr(100) = 5772 and Tr(1000) = 11174776.
|
||
|
|
|
||
|
|
Find Tr(60 000 000). Give the last 18 digits of your answer.
|
||
|
|
|
||
|
|
# --hints--
|
||
|
|
|
||
|
|
`euler378()` should return 147534623725724700.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.strictEqual(euler378(), 147534623725724700);
|
||
|
|
```
|
||
|
|
|
||
|
|
# --seed--
|
||
|
|
|
||
|
|
## --seed-contents--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function euler378() {
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
euler378();
|
||
|
|
```
|
||
|
|
|
||
|
|
# --solutions--
|
||
|
|
|
||
|
|
```js
|
||
|
|
// solution required
|
||
|
|
```
|